因数 ax^2-ay-bx^2+cy+by-cx^2

解

因数

a x^{2} - a y - b x^{2} + cy + b y - c x^{2}

(x^{2} - y) (a - b - c)

解答ステップ

a x^{2} - a y - b x^{2} + cy + b y - c x^{2}

共通項をくくり出す

a

= a (x^{2} - y) - b x^{2} + cy + b y - c x^{2}

共通項をくくり出す

b

= a (x^{2} - y) + b (- x^{2} + y) + cy - c x^{2}

書き換え

= (x^{2} - y) a - (x^{2} - y) b + cy - c x^{2}

共通項をくくり出す

(x^{2} - y)

= (x^{2} - y) (a - b) + cy - c x^{2}

共通項をくくり出す

c

= (x^{2} - y) (a - b) + c (y - x^{2})

書き換え

= (x^{2} - y) (a - b) - (x^{2} - y) c

共通項をくくり出す

(x^{2} - y)

= (x^{2} - y) (a - b - c)